Abstract
Abstract Amplitude vacillation is studied using a spectral version of the two-level quasi-geostrophic model in a β-plane channel. The parameters are chosen so that only a single wave may be unstable to the undisturbed basic state. It is shown that the weakly nonlinear theories which have been proposed do not work well on the β-plane, because nonlinear interactions are not negligible even though only a single wave has any significant amplitude. The energetics and mechanism of amplitude vacillation on a β-plane are discussed for a case with moderate dissipation and contrasted with the mechanism on an f-plane.
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